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GCF of 321/73, 618/189

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 321/73, 618/189 i.e 3/13797 easily. The following is the detailed procedure to determine the greatest common factor of fractions 321/73, 618/189.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 321/73,618/189?

Given fractions are 321/73,618/189

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 321/73,618/189, numerators are 321,618

Denominators are 73,189

The GCF of 321,618 is 3 .

LCM of 73,189 is 13797.

The greatest common factor of 321/73,618/189 = [GCF of 321,618]/[LCM of 73,189]= 3/13797

Therefore, the GCF of 321/73,618/189 is 3/13797.

Greatest Common Factor of 321,618

To find the highest common factor of 321,618, we have to find the factors of both numbers and list the highest common factor.

The factors of 321 are 1, 3, 107, 321

The factors of 618 are 1, 2, 3, 6, 103, 206, 309, 618

The HCF of 321,618 is 3.

Lets's calculate GCF of 321,618

Greatest Common Factor (GCF) of 321,618 By Common Division

3 321, 618
107, 206

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 321,618 By Matching Biggest Common Factor Method

Greatest Common Factor of 321,618 By Matching Biggest Common Factor Method

Now, list down the factors of 321

:

1,3,107,321

Now, list down the factors of 618

:

1,2,3,6,103,206,309,618

Greatest Common Factor

We found the factors 321,618 . The biggest common factor number is the GCF number.
So the greatest common factor 321,618 is 3.

Lets's calculate LCM of 73,189

Lowest Common Multiple of 73,189 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 13797

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/13797

Therefore, the GCF of Fractions 321/73,618/189 is 3/13797

Least Common Multiple of 73,189 with GCF Formula

Least Common Multiple of 73,189 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 73,189 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(73,189) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(73,189) x common factors =1 x 1 = 1

LCM(73,189) = ( 73 × 189 ) / 1

LCM(73,189) = 13797 / 1

LCM(73,189) = 13797


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FAQs on GCF of Fractions of 321/73, 618/189

1. What is the HCF of 321,618?

The HCF of 321,618 is 3

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 321/73, 618/189?

Answer: GCF of Numerators as per given numbers 321/73, 618/189 is

GCF of Numerators i.e. for 321,618 is 3

LCM of denominators i.e. for 73,189 is 13797.

Thus, GCF of Fractions is 3/13797.Finally, GCF of Fractions for 321/73, 618/189 is 3/13797.